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# A group consists of both men and women. The average (arithmetic mean)

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 00:31
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Difficulty:

25% (medium)

Question Stats:

66% (01:07) correct 34% (01:26) wrong based on 51 sessions

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A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

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Joined: 30 Aug 2018
Posts: 4
Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 00:57
C. 2:1
(66x + 72y)/(x+y) = 70
66x + 72y =70x + 70y
66x-70x = 70y-72y
-4x=-2y
2:1

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Joined: 30 Aug 2018
Posts: 4
Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 00:58
C. 2:1
(66x + 72y)/(x+y) = 70
66x + 72y =70x + 70y
66x-70x = 70y-72y
-4x=-2y
2:1

Posted from my mobile device
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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1013
WE: Supply Chain Management (Energy and Utilities)
Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 01:05
1
Bunuel wrote:
A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

Sum of heights of women=66*w
Sum of heights of men=72*m
Sum of heights of the group(men+women)= 70*(m+w)

To find:- w:m=?

Now, Sum of height of men+sum of height of women=Sum of heights of the group
or, 66w+72m=70*(m+w)
or, 2m=4w
Or, w:m=1:2

Ans. (B)
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Concentration: Accounting, Finance
GPA: 3.68
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Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 06:20
1
Bunuel wrote:
A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

Using Allegation Method , one can solve this question in 20 sec...........
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Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 06:41
Bunuel wrote:
A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

$$66w + 72m = 70m + 70w$$

Or, $$4w = 2m$$

Or, $$w : m = 1 : 2$$, Answer must be (B)
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VP
Joined: 09 Mar 2016
Posts: 1230
A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 07:08
Bunuel wrote:
A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

let #number of males be M
let #number of females be F
let number of all people be X

average (arithmetic mean) height of the women is 66 inches $$\frac{X}{F} = 66$$ --- > X= 66F (1)

average (arithmetic mean) height of the men is 72 inches $$\frac{X}{M}= 72$$ ---- > X=72M (2)

average (arithmetic mean) height of all the people in the group is 70 inches $$\frac{X}{M+F} = 70$$ (plug in X1 and X2 here )

$$\frac{66F+72M}{M+F} = 70$$

$$66F+72M = 70(M+F)$$

$$66F+72M = 70M+70F$$

$$2M=4F$$

$$1M=2F$$
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Posts: 1230
Re: A group consists of both men and women. The average (arithmetic mean)  [#permalink]

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30 Aug 2018, 07:11
selim wrote:
Bunuel wrote:
A group consists of both men and women. The average (arithmetic mean) height of the women is 66 inches, and the average (arithmetic mean) height of the men is 72 inches. If the average (arithmetic mean) height of all the people in the group is 70 inches, what is the ratio of women to men in the group?

(A) 1:1
(B) 1:2
(C) 2:1
(D) 2:3
(E) 3:2

Using Allegation Method , one can solve this question in 20 sec...........

thanks for reminding me alligator method
Re: A group consists of both men and women. The average (arithmetic mean)   [#permalink] 30 Aug 2018, 07:11
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